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Peter Athron David Miller In collaboration with Quantifying Fine Tuning (arXiv:0705.2241)

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Outline Motivations for supersymmetry Hierarchy problem Little Hierarchy Problem Traditional Tuning Measure New tuning measure ESSM EWSB in the ESSM

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Supersymmetry The only possible extension to space-time Unifies gauge couplings Provides Dark Matter candidates Leptogenesis in the early universe Elegant solution to the Hierarchy Problem! Essential ingredient for M-Theory

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Expect New Physics at Planck Energy (Mass) Hierarchy Problem Higgs mass sensitive to this scale Supersymmetry (SUSY) removes quadratic dependence Enormous Fine tuning! SUSY? Standard Model (SM) of particle physics Eliminates fine tuning Beautiful description of Electromagnetic, Weak and Strong forces Neglects gravitation, very weak at low energies (large distances)

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Little Hierarchy Problem Constrained Minimal Supersymmetric Standard Model (CMSSM) Z boson mass predicted from CMSSM parameters Fine tuning?

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Superymmetry Models with extended Higgs sectors NMSSM nMSSM E 6 SSM Supersymmetry Plus Little Higgs Twin Higgs Alternative solutions to the Hierarchy Problem Technicolor Large Extra Dimensions Little Higgs Twin Higgs Need a reliable, quantitative measure of fine tuning to judge the success of these approaches. Solutions?

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J.R. Ellis, K. Enqvist, D.V. Nanopoulas, & F.Zwirner (1986) R. Barbieri & G.F. Giudice, (1988) Define Tuning is fine tuned % change in from 1% change in Observable Parameter Traditional Measure

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Limitations of the Traditional Measure Considers each parameter separately Fine tuning is about cancellations between parameters. A good fine tuning measure considers all parameters together. Implicitly assumes a uniform distribution of parameters Parameters in L GUT may be different to those in L SUSY parameters drawn from a different probability distribution Takes infinitesimal variations in the parameters Observables may look stable (unstable) locally, but unstable (stable) over finite variations in the parameters. Considers only one observable Theories may contain tunings in several observables Global Sensitivity (discussed later)

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parameter space volume restricted by, Parameter space point, Unnormalised Tuning: New Measure `` Compare dimensionless variations in ALL parameters With dimensionless variations in ALL observables

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Global Sensitivity Consider: responds sensitively to All values of appear equally tuned! throughout the whole parameter space (globally) All are atypical? True tuning must be quantified with a normalised measure G. W. Anderson & D.J Castano (1995) Only relative sensitivity between different points indicates atypical values of

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parameter space volume restricted by, Parameter space point, Unnormalised Tunings New Measure Normalised Tunings mean value `` `` AND

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Probability of random point lying in : Probability of a point lying in a “typical” volume: New Measure Define: We can associate our tuning measure with relative improbability! volume with physical scenarios qualitatively “similar” to point P

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Standard Model Obtain over whole parameter range:

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Choose a point P in the parameter space at GUT scale Take random fluctuations about this point. Using a modified version of Softsusy (B.C. Allanach) Run to Electro-Weak Symmetry Breaking scale. Predict M z and sparticle masses Count how many points are in F and in G. Apply fine tuning measure Fine Tuning in the CMSSM

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For our study of tuning in the CMSSM we chose a grid of points: Plots showing tuning variation in m 1/2 were obtained by taking the average tuning for each m 1/2 over all m 0. Plots showing tuning variation in m 0 were obtained by taking the average tuning for each m 0 over all m 1/2. Technical Aside To reduce statistical errors:

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Tuning in

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Tuning

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m 1/2 (GeV)

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“Natural” Point 1

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“Natural” Point 2

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If we normalise with NP1If we normalise with NP2 Tunings for the points shown in plots are:

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Naturalness comparisons of BSM models need a reliable tuning measure, but the traditional measure neglects: Many parameter nature of fine tuning; Tunings in other observables; Behaviour over finite variations; Probability dist. of parameters; Global Sensitivity. New measure addresses these issues and: Demonstrates and increase with. Naïve interpretation: tuning worse than thought. Normalisation may dramatically change this. If we can explain the Little hierarchy Problem. Alternatively a large may be reduced by changing parameterisation. Could provide a hint for a GUT. Fine Tuning Summary

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Electroweak Symmetry Breaking in the E 6 SSM Peter Athron In collaboration with S.F. King, D.J. Miller, S. Moretti & R. Nevzorov.

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Exceptional Supersymmetric Standard Model (Phys.Rev. D73 (2006) 035009 arXiv:hep-ph/0510419, Phys.Lett. B634 (2006) 278-284 arXiv:hep-ph/0511256 S.F.King, S.Moretti & R. Nevzorov ) arXiv:hep-ph/0510419 arXiv:hep-ph/0511256 Exotic coloured matter 3 generations of Singlet fields Ordinary matter E 6 inspired model with an extra gauged U(1) symmetry Matter content based on 3 generations of complete 27plet representations of E 6 ) anomalies automatically cancelled Provides a low energy alternative to the MSSM and NMSSM 3 generations of Higgs like fields Extra SU(2) doublets (for gauge coupling unification)

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E 6 SSM Superpotential S = S 3 develops vev, h S i = s, giving mass to exotic coloured fields H u = H 2,3 & H d = H 1,3 develop vevs, h H 0 u i =v u & h H 0 d i =v d Give mass to ordinary matter via Higgs Mechanism generates an effective term Solves -problem of MSSM as in NMSSM without tadpoles/domain walls problems

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ESSM NMSSM MSSM Two Loop Upper Bounds on the Light Higgs

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NUHESSM GUT-scale universality assumptions Highscale mass for all other scalar fields Highscale mass for three generations of Singlet fields Highscale mass for three generations of H 2 fields Highscale mass for three generations of H 1 fields Universal Gaugino Mass Universal trilinear soft mass Minimal supergravity inspired GUT-scale constraints on parameters

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EWSB constraints Scalar masses Gaugino masses Trilinear soft masses Solutions must possess symmetry Obtain RGE solutions for soft masses at EW scale Fix v 2 = v u 2 + v d 2 = (174 GeV) 2 Choose Yukawas 3 =0.6; 1,2 =0.46; 1,2,3 =0.162 Choose tan = v u /v d = 10, s = 3 TeV

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EWSB constraints AllowedEW tachyonsGUT tachyonsExperimentally ruled out

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Sample Spectrum

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Conclusions Solutions with all universal masses are hard to find. Allow non universal Higgs masses. Dramatic improvement! Many spectrums which could be seen at the LHC. RGE solutions ) Gluino often lighter than the squarks Further work: Include two loop RGEs for gaugino masses Look for solutions with stronger universality assumptions

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1 loop RGE solutions for fully universal benchmark point

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